The heart acts as the pump for the human circulatory system, providing the energy that enables the blood to move through the body. The heart does work in pumping the blood, and this work is manifested in the blood pressure and in the kinetic energy of the blood as it flows through the arteries. In the human body under low-stress rest conditions, nearly all the work done by the heart can be thought of as providing the average blood pressure in the arteries. Under these conditions, the power output of the heart is given by the equation P = π Q, where π is the average blood pressure and Q is the volume flow rate.

In a normal, healthy person, the average blood pressure is about 100 mm Hg, and blood flow through the arteries can be considered to be ideal. Blood leaves the heart through the aorta, which has cross-sectional area, A, of about 3 cm 2 . The artiries are flexible and can dilate or constrict to regulate blood flow. Certain conditions, such as those brought on by high cholesterol intake or heavy smoking, can cause the arteries to become occluded. As the available cross-sectional area of the arteries is decreased, the heart must provide increased pressure in order to maintain a sufficient volume of blood flow. Figure given below shows the effect of decreased arterial radius on blood pressure. Arteries can be assumed to have circular cross-sections.

Blood pressure vs. arterial radius

Typical volume flow rate for blood in a person at rest is about 100 cm 3 /sec

Volume rate of flow Q = Av = constant:

A → Area of cross-section of Artery,

v → flow speed of blood

(Note: 10 5 N/m 2 760 mm Hg)

(i) The pulse rate for an average healthy person at rest is about 75 beats/minute. What is the average volume pumped per heart beat for this person –